Shallow water waves over polygonal bottoms

Mathieu Cathala (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

The traditional shallow water model for waves propagating over varying bathymetry depends for its derivation on the asymptotic analysis of a Dirichlet-Neumann operator. This analysis however is restricted to smoothly varying topographies. We propose an adaptation to one dimensional polygonal bottoms using the conformal mapping idea of Hamilton and Nachbin. The asymptotic analysis of the Dirichlet-Neumann operator relies on an ad hoc transformation of the fluid domain into a flat bottom domain. We derive a new shallow water model which accounts for polygonal topographies.

Mots clés: Water waves; shallow water models; non smooth bathymetry; Dirichlet-Neumann operator

Domaines: Equations aux dérivées partielles [math.AP]

Mathieu Cathala. Shallow water waves over polygonal bottoms. 2013. ⟨hal-00847843v2⟩